QOJ.ac
QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#683807 | #9520. Concave Hull | susanzhishen | AC ✓ | 229ms | 49100kb | C++20 | 6.9kb | 2024-10-27 23:59:13 | 2024-10-30 01:33:58 |
Judging History
answer
#include<bits/stdc++.h>
#define int long long
#define double long double
#define x first
#define y second
using namespace std;
typedef long long LL;
typedef long long ll;
typedef pair<int,int> PII;
#define db double
const db eps = 1e-12;
const db inf = 1e20;
const db PI = acos(-1.0);
inline int sgn(db x) {return x < -eps ? -1 : x > eps;}
inline db sqr(db x) { return x*x; }
inline db mysqrt(db x) { return sqrt(max((double)0.0, x)); }
//注意y1给系统占了
const int N=3e5+10;
const int M=1e3+10;
int mod=1e9+7;
/*========================================================*\
| Point 类
| 类内函数
| Point(P x = 0, P y = 0) - 默认构造函数
| input() - 读入一个点
| operator == - NULL
| operator < - 用于排序
| operator + - 返回Point
| operator - - 返回Point
| operator * - 返回Point
| operator / - 返回Point
| len() - 返回长度
| len2() - 返回长度平方
| trunc(db len) - 长度变为len
| rotleft() - 逆时针转π/2, 返回Point
| rotright() - 顺时针转π/2, 返回Point
| rotate(P p, db ang) - 绕p逆时针转ang
| 类外函数
| *基础功能
| Cross(P a, P b) - NULL
| Cross(P pt, P a, P b) - NULL
| Dot(P a, P b) - NULL
| Dot(P pt, P a, P b) - NULL
| Dist(P a, P b) - NULL
| Len(a) - 返回a的长度
| Len2(a) - 返回a的长度平方
| rad(P p, P a, P b) - 返回∠apb
| Complex类补充
\*========================================================*/
struct Point {
db x, y;
Point (db x=0, db y=0): x(x), y(y) {}
void input() { scanf("%lf%lf", &x, &y); }
bool operator == (Point r) { return sgn(x-r.x)==0 && sgn(y-r.y)==0; }
// bool operator < (Point r) { return sgn(x-r.x)==0 ? y < r.y : x < r.x; }
Point operator + (Point r) { return Point (x+r.x, y+r.y); }
Point operator - (Point r) { return Point (x-r.x, y-r.y); }
Point operator * (db r) { return Point (x*r, y*r); }
Point operator / (db r) { return Point (x/r, y/r); }
db len() { return mysqrt(x*x+y*y); }
db len2() { return x*x + y*y; }
// 化为长度为 r 的向量
Point trunc(db len) {
db l = mysqrt(x * x + y * y);
if (! sgn(l)) return *this;
len /= l;
return Point (x*len, y*len);
}
// 逆时针旋转 90 度
Point rotleft() { return Point (-y, x); }
// 顺时针旋转 90 度
Point rotright() { return Point (y, -x); }
// 绕着 p 点逆时针旋转 ang
Point rotate (Point p, db ang) {
Point v = (*this) - p;
db c = cos(ang), s = sin(ang);
return Point (p.x + v.x*c - v.y*s, p.y + v.x*s + v.y*c);
}
};
/******************************\
| 基础功能
\******************************/
db Cross (Point a, Point b) { return a.x*b.y - a.y*b.x; }
db Cross (Point pt, Point a, Point b) { return Cross(a-pt, b-pt); }
db Dot (Point a, Point b) { return a.x*b.x + a.y*b.y; }
db Dot (Point pt, Point a, Point b) { return Dot (a-pt, b-pt); }
db Dist (Point a, Point b) { return mysqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)); }
db Len (Point a) { return mysqrt(a.x*a.x + a.y*a.y); }
db Len2 (Point a) { return a.x*a.x + a.y*a.y; }
// 计算 pa 和 pb 的夹角, 就是求这个点看 a, b 所成的夹角, 测试 LightOJ 1203
db rad(Point p, Point a, Point b) {
return fabs(atan2(fabs(Cross(p, a, b)), Dot(p, a, b) ));
}
/******************************\
| Complex补充
\******************************/
struct Complex {
db x, y;
Complex(db x = 0, db y = 0) : x(x), y(y) {}
Complex operator + (Complex b) {return Complex(x + b.x, y + b.y);}
Complex operator - (Complex b) {return Complex(x - b.x, y - b.y);}
Complex operator * (Complex b) {return Complex(x * b.x - y * b.y, x * b.y + y * b.x);}
};
// db disptl(Line v, Point p) {
// return fabs(Cross(v.s, p, v.e)) / v.length(); // length = [](){return Dist(v.s, v.e);}
// }
// Andrew 算法
// 坐标排序 O(nlogn), 测试: 洛谷P2742;凸包稳定相关: POJ1228
// 这里有两种排序方法
// 1. 优先按 y 排序, 如果 y 相同, 按 x 排序, 起点是最下面的点, 如下面代码体现
// 2. 优先按 x 排序, 如果 x 相同, 按 y 排序, 起点是最左边的点
bool operator < (Point a, Point b) {
if (sgn(a.y - b.y) == 0) return a.x < b.x;
return a.y < b.y;
}
int andrew(Point *p, Point *ch, int n) { // 返回值是凸包的顶点数
sort (p, p + n); // 排序
n = unique(p, p + n) - p; // 去除重复的点
int v = 0;
// 求下凸包, 如果 p[i] 是右拐弯的, 则这个点不在凸包中, 往回退
for (int i = 0; i < n; i ++) {
while (v > 1 && sgn(Cross(ch[v-2], ch[v-1], p[i])) <= 0) v --;
ch[v ++] = p[i];
}
int j = v;
// 求上凸包
for (int i = n - 2; i >= 0; i --) {
while (v > j && sgn(Cross(ch[v-2], ch[v-1], p[i])) <= 0) v --;
ch[v ++] = p[i];
}
if (n > 1) v --;
return v;
}
db area(Point a, Point b, Point c){
Point AB=b-a,AC=c-a;
return fabs(AB.x*AC.y-AB.y*AC.x);
}
db polygonarea(Point* p, int n) {
db ans = 0;
p[n] = p[0];
for (int i = 0; i < n; i ++)
ans += Cross(p[i], p[i+1]);
return fabs(ans) ; // 面积有正负, 需根据题意来判断要不要取绝对值
}
db disptl(Point A, Point B, Point p) {
return fabs(Cross(A, p, B)) / Dist(A, B); // length = [](){return Dist(v.s, v.e);}
}
Point ch1[N], ch2[N],p1[N],p2[N];
int vis[N];
void solve(){
int n;cin>>n;
for(int i=0;i<=n;i++) p1[i].x=p1[i].y=p2[i].x=p2[i].y=ch1[i].x=ch1[i].y=ch2[i].x=ch2[i].y=vis[i]=0;
map<PII,int>mp;
for(int i=0;i<n;i++) cin>>p1[i].x>>p1[i].y;
int m1 = andrew(p1, ch1, n);
if(m1==n){
cout<<"-1\n";
return ;
}
for(int i=0;i<n;i++) mp[{p1[i].x,p1[i].y}]=i;
// cout<<"\n";
for(int i=0;i<m1;i++){
vis[mp[{ch1[i].x,ch1[i].y}]]=1;
}
int sp=0;
for(int i=0;i<n;i++){
if(!vis[i]) p2[sp++]=p1[i];
// cout<<vis[i]<<" ";
}
int m2 = andrew(p2, ch2, sp);
double S=polygonarea(ch1, m1);
int idx=0;
double ans=0;
// cout<<"\n";
for(int i=0;i<m1;i++){
double fz=1e19,mu=1;
Point A=ch1[i],B=ch1[(i+1)%m1];
while(1){
double fz1=fabs(Cross(A,B,ch2[idx]))*fabs(Cross(A,B,ch2[idx]));
double mu1=(A.x-B.x)*(A.x-B.x)+(A.y-B.y)*(A.y-B.y);
if(fz1*mu<fz*mu1) fz=fz1,mu=mu1;
else break;
idx=(idx+1)%m2;
}
idx=(idx-1+m2)%m2;
ans=max(ans,S-area(A,B,ch2[idx]));
}
cout<<(int)ans<<"\n";
}
signed main(){
// ios::sync_with_stdio(false);
// cin.tie(nullptr),cout.tie(nullptr);
int _;
_=1;
cin>>_;
while(_--){
solve();
}
}
这程序好像有点Bug,我给组数据试试?
详细
Test #1:
score: 100
Accepted
time: 3ms
memory: 42188kb
input:
2 6 -2 0 1 -2 5 2 0 4 1 2 3 1 4 0 0 1 0 0 1 1 1
output:
40 -1
result:
ok 2 lines
Test #2:
score: 0
Accepted
time: 11ms
memory: 41900kb
input:
10 243 -494423502 -591557038 -493438474 -648991734 -493289308 -656152126 -491185085 -661710614 -489063449 -666925265 -464265894 -709944049 -447472922 -737242534 -415977509 -773788538 -394263365 -797285016 -382728841 -807396819 -373481975 -814685302 -368242265 -818267002 -344482838 -833805545 -279398...
output:
2178418010787347715 1826413114144932145 1651687576234220014 1883871859778998985 2119126281997959892 894016174881844630 2271191316922158910 1998643358049669416 1740474221286618711 1168195646932543192
result:
ok 10 lines
Test #3:
score: 0
Accepted
time: 106ms
memory: 41836kb
input:
1000 125 64661186 -13143076 302828013 -185438065 -418713797 -191594241 430218126 -397441626 354327250 -836704374 149668812 -598584998 311305970 66790541 199720625 -592356787 468137 -584752683 258775829 96211747 -358669612 -134890109 -129221188 -998432368 -277309896 -140056561 356901185 420557649 -51...
output:
1986320445246155278 1900093336073022078 1612088392301142476 2012259136539173407 1819942017252118749 1772230185841892196 1164835025329039520 1527446155241140517 1807368432185303666 1236918659444944569 1306839249967484778 1984123720246784099 1868728080720036006 667458140583450322 2127932992585026491 4...
result:
ok 1000 lines
Test #4:
score: 0
Accepted
time: 142ms
memory: 41348kb
input:
10000 9 484630042 51929469 -40468396 -517784096 98214104 -103353239 629244333 -475172587 106398764 153884485 49211709 -44865749 1 10 166321833 -247717657 406208245 668933360 13 548702216 -631976459 37150086 -292461024 707804811 -486185860 239775286 -903166050 10096571 -541890068 686103484 558731937 ...
output:
950319193795831919 1661025342421008544 1285164852091455548 1159924751776806668 1206071151805176722 794021230296144371 699991678992587791 1133990718508584290 1486311831172661605 984875884297072200 1327767982175057345 758247019006396699 1355381234262206155 1139262078529131471 1613462877860621700 12392...
result:
ok 10000 lines
Test #5:
score: 0
Accepted
time: 229ms
memory: 42328kb
input:
100 439 471536154 -312612104 155692036 -937312180 -461624056 -357636609 236656684 -911414873 -288656914 -74788431 -465779694 -381475149 -334197401 -903065737 491513067 -447615916 337664889 -852236281 -281689379 -53519178 -159101704 -920779200 -326159514 -95396204 21868593 -994282736 488425383 -41046...
output:
1973162724053130487 2054612790507830954 1726805687754843724 1699420177872986528 2129388571309147631 2198295137903288810 1697185883164440272 1219697450095721478 2027023581922285255 1674691247127206655 1673105966817209954 2179188692918747442 2146544318743443141 2230356305133660648 1676850321902993764 ...
result:
ok 100 lines
Test #6:
score: 0
Accepted
time: 198ms
memory: 43312kb
input:
100 1362 -467257672 -466669 -467054869 -478108 -466973270 -481776 -466556983 -499770 -466329414 -508693 -466248017 -511805 -466158865 -513786 -466101273 -515035 -465927700 -518748 -465717624 -522106 -465303448 -528127 -465124548 -530726 -464649746 -536693 -464554872 -537799 -464478196 -538680 -46416...
output:
1666097696993497 1791366071767866 1806187278469532 1683419854733713 1685891971828916 1730190225081651 1787048201197565 1850308098208660 1710694884375502 1826363113637639 1816375352374659 2047431269497691 1549806516003854 1829438662895747 1678707854135065 1687423392883819 2121960009997761 16687219538...
result:
ok 100 lines
Test #7:
score: 0
Accepted
time: 114ms
memory: 46724kb
input:
2 62666 -486101704 -505730259 -486101698 -506082699 -486101689 -506111362 -486101682 -506126031 -486101528 -506293759 -486101259 -506556385 -486101196 -506613483 -486101154 -506648604 -486100935 -506831392 -486100631 -507083675 -486100470 -507199151 -486100233 -507368923 -486100193 -507397039 -48609...
output:
2178736946152219010 1825181940245096152
result:
ok 2 lines
Test #8:
score: 0
Accepted
time: 228ms
memory: 48888kb
input:
2 100000 301945097 76373292 467957663 -286424714 8245445 -597212507 -474204621 -708828667 184159460 105942538 443435905 -429212625 490658771 -382198656 82512047 -612522436 -228221388 -965890088 394789011 -145801151 -106120174 -528202395 428939626 -194437311 497429477 -527407728 365739746 -114818962 ...
output:
2502889432701099511 2267250485735988121
result:
ok 2 lines
Test #9:
score: 0
Accepted
time: 228ms
memory: 49100kb
input:
2 100000 221128057 -975244780 -618765360 -785575858 422567455 -906331476 -988680318 -150037424 -929870145 367887908 -757813541 -652471177 291995621 -956419655 -785381507 619012026 468864522 -883270094 -588416522 808557973 859345881 511394814 988105866 153775152 216931298 -976186873 467050734 8842305...
output:
6283183114882825575 6283183188903854361
result:
ok 2 lines
Test #10:
score: 0
Accepted
time: 13ms
memory: 41344kb
input:
7 5 -1000000000 -1000000000 1000000000 -1000000000 1000000000 1000000000 1 0 -1 0 5 1000000000 1000000000 -1000000000 -1000000000 -2 0 -1 0 1 -1 6 1000000000 1000000000 -1000000000 -1000000000 -3 0 -1 0 0 -1 1 -1 4 -1000000000 -1000000000 1000000000 -1000000000 1000000000 1000000000 -1000000000 1000...
output:
4000000000000000000 7000000000 9000000001 -1 6000000002000000000 7999999998000000000 -1
result:
ok 7 lines
Extra Test:
score: 0
Extra Test Passed